Genetic association studies conducted through the 'genome--wide era' have failed to explain more than a modest fraction of the estimated heritability of most complex traits. This has been ascribed to their limited power and scope born of a focus on the marginal effects of common variants. The NCI's Cancer Post--GWAS Initiative typifies the new paradigm, one focused on moving past these limitations. This new generation of association study raises pressing analytical challenges. These include: (I), maintaining power to reliably detect and localize gene by environment (G*E) interactions in the face of a very large number of statistical tests and given the very real potential for study--to-- study heterogeneity in effects; (II), formally incorporating functional annotation variables into the association analyses in a way that accounts for the ability of certain of the variables to explain previous associations and that is flexible enough to account for new variables specific to the disease and/or exposure of interest; and, (III) overcoming computational barriers to analysis plans that address the above challenges at the scale of implementation that is required. In answer to these, we will develop and implement statistically and computationally efficient Bayesian analytic strategies for consortium level studies of the role played by gene- environment interaction in complex disease. In particular, we will: (1) develop Bayesian models and model search for consortium level analysis of G*E interaction in complex disease; (2) develop locus inclusion prior distributions that depend on functional annotation data through functional 'signatures;' and (3) develop and test computationally efficient, portable and open source software implementations of these methods tuned to harness the full potential of graphical processing unit (GPU) equipped and multicore workstations and thereby achieve significant speed gains over more traditional implementations. PUBLIC HEALTH RELEVANCE: The primary motivation behind genetic association studies is the expectation that they will uncover information that will contribute to public health both in the near-term, by identifying factors that will help identify groups of individuals at high risk for disease, and in the longer term, by improving our understanding of the biological mechanisms behind disease in a way that will lead to improved treatments and/or preventative strategies. Association studies in the 'Post-GWAS' era raise new analytical challenges that must be met before their full potential, and their public health benefits, are realized. The program of research that we propose addresses these analytic challenges.